Worksheet: Grouped Frequency Tables

In this worksheet, we will practice reading and interpreting frequency tables and tally charts and forming a frequency table for a given quantitative data set.

Q1:

The table shows the marks out of 10 that students scored in a test. How many students scored higher than the modal mark?

Mark 5 6 7 8 9 10
Frequency 3 1 18 12 10 5
  • A22 students
  • B45 students
  • C27 students
  • D18 students
  • E4 students

Q2:

The tally chart shows the marks that students in a class received in a mathematics test. Using the information from the tally chart, complete the frequency table.

Sets 5– 10– 15– 20– 25–
Tally
Sets 5– 10– 15– 20– 25–
Frequency
  • A 1 0 , 1 4 , 1 2 , 1 6 , 6
  • B 9 , 1 4 , 1 2 , 1 6 , 6
  • C 9 , 1 5 , 1 2 , 1 6 , 6
  • D 8 , 1 3 , 1 1 , 1 5 , 5
  • E 9 , 1 4 , 1 2 , 1 5 , 6

Q3:

The table shows the number of classes of varying sizes in a school. Using the data, complete the frequency table.

Class Size 16 17 18 19 20 21
Number of Classes 4 2 3 5 1 4
Class Size 16-17 18-19 20-21
Frequency
  • A9, 9, 10
  • B9, 8, 5
  • C6, 8, 5
  • D6, 5, 9

Q4:

The table shows the marks of 100 students in a recent science exam. How many students received 40 marks or more?

Mark 0–9 10–19 20–29 30–39 40–49 50– Total
Frequency 6 15 12 26 23 18 100

Q5:

The frequency table below shows the weights of 40 students in a class. How many students weigh less than 50 kg?

Weight, 𝑤 30– 35– 40– 45– 50– Total
Frequency 5 8 12 9 6 40

Q6:

The table shows the heights of 100 students in a school. How many students’ heights are greater than or equal to 120 cm?

Height (cm) 115–119 120–124 125–129 130–134 135–139 140–144 145– Total
Number of Students 12 12 20 16 12 10 18 100

Q7:

The table shows the marks of 60 students in a science exam. How many students failed the test given that the pass mark was 30?

Marks 0–9 10–19 20–29 30–39 40–49 50– Total
Frequency 3 18 10 8 15 6 60

Q8:

The table shows the marks that a class of students received in their mathematics test. How many students are in the class?

Marks 0–1 2–3 4–5 6–7 8–
Frequencies 8 4 5 2 10

Q9:

Complete the frequency table which shows the marks a group of students received in a test.

Marks 20–24 25–29 30–34 35–39 40–44 45–49 50– Total
Frequency 4 5 15 9 10 4 50

Q10:

The tally chart shows the marks students received in a mathematics test. How many students received less than 10 marks?

Mark 5–9 10–14 15–19 20–24 25–29
Frequency

Q11:

The table shows the number of days each student has been absent. Use this data to complete the frequency table.

6 4 0 5 4 2 2 2 6 4
1 3 2 6 6 3 0 1 6 1
4 5 0 4 6 1 3 6 3 1
1 5 2 6 3 5 1 6 6 0
Number of Days Absent 0 1 2 3 4 5 6
Frequency
  • A 4 , 7 , 5 , 5 , 5 , 4 , 1 0
  • B 5 , 7 , 5 , 5 , 5 , 4 , 1 0
  • C 5 , 7 , 5 , 6 , 5 , 4 , 1 0
  • D 4 , 8 , 5 , 5 , 5 , 3 , 1 0
  • E 4 , 7 , 4 , 5 , 4 , 4 , 1 0

Q12:

Using the data given for number of absences, complete the frequency table.

7 10 7 8 5 1 2 7
6 2 4 3 2 8 5 6
5 8 9 8 2 1 10 9
10 9 10 3 9 7 7 8
Number of Absences 1-2 3-4 5-6 7-8 8–10
Frequency
  • A 3 , 6 , 5 , 8 , 1 0
  • B 6 , 3 , 5 , 1 0 , 8
  • C 8 , 1 0 , 5 , 3 , 6
  • D 1 0 , 8 , 5 , 3 , 6

Q13:

The table of numbers shows the marks of 30 students in a mathematics exam.

25 37 31 39 26 23 27 31 20 33
35 37 23 37 21 33 24 27 36 27
32 26 30 37 25 31 32 21 28 32

Using this data, complete the frequency table.

Marks 20–23 24–27 28–31 32–35 36– Total
Frequency 30
  • A4, 7, 4, 3, 5
  • B5, 8, 5, 6, 6
  • C6, 8, 7, 4, 5
  • D6, 9, 8, 7, 6
  • E3, 7, 5, 8, 7

Q14:

The table of data shows the heights in centimeters of teachers at a school. Using a frequency table, find the number of teachers who are 175 cm or more.

179 169 193 171 163 186 178 173
167 166 195 156 163 190 171 195
156 186 187 159 172 169 184 195
159 168 179 155 178 162 174 167
193 177 159 179 162 189 163 182
181 167 189 173 187 159 170 186

Q15:

The table shows the number of days taken off work by 40 workers in a year. By constructing a frequency table or otherwise, calculate the number of workers who took 20 or more days off work.

16 18 5 20 15 26 12 17 8 5
5 12 26 30 23 22 21 30 25 21
27 15 12 28 11 12 26 12 13 23
6 29 28 5 20 12 10 24 23 14

Q16:

The table shows the weekly wages of 30 workers in a factory. By forming the frequency table using the intervals 30–39, 40–49, 50–59, 60–69, 70–79, 80–89, and 90–99, find which interval has the highest frequency.

43 47 43 99 54 47 53 100 46 97
50 41 36 72 38 37 80 46 74 74
30 34 32 97 90 35 68 87 78 30
  • A60–69
  • B50–59
  • C40–49
  • D30–39

Q17:

The table shows the marks that a class of students received in a mathematics test. How many students got less than 45 marks?

Marks 20–24 25–29 30–34 35–39 40–44 45–49 50–54 55– Total
Number of Students 7 8 2 5 6 5 9 2 44

Q18:

Complete the frequency table by finding the value of 𝑥.

Sets 10-19 20-29 30-39 40-49 𝑥 -59 60-69 Total
Frequency 3 13 6 8 11 9 50

Q19:

The table shows the marks of 100 students in a recent science exam. What percentage of students received 20 marks or more?

Mark 0– 10– 20– 30– 40– 50– Total
Frequency 5 25 21 16 19 14 100

Q20:

Given an interval with lower limit 16 and center 23, find the upper limit of the interval.

Q21:

The table shows donations made by students to a charity. How many students donated between 60–70 pounds?

Donation in Pounds 20–29 30–39 40–49 50–59 60–69 70– Total Number of Students
Number of Students 4 2 3 7 16 5 37

Q22:

The table shows the distribution of exam marks in science for 1‎ ‎000 students. By drawing a cumulative frequency curve, determine the number of students who scored 54 marks or more.

Scores 20–29 30–39 40–49 50–59 60–69 70–79 80–89 90–99 Total
Frequency 105 134 124 130 119 156 110 122 1‎ ‎000
  • A637 students
  • B585 students
  • C631 students
  • D124 students
  • E507 students

Q23:

The table shows the bonuses received by 75 factory workers. How many workers received a bonus which was less than 50 LE?

Bonus (LE) 20–29 30–39 40–49 50–59 60–69 70– Total
Number of Workers 10 5 10 15 25 10 75

Q24:

The scores that 30 students achieved in a maths exam are shown in the table. By constructing a frequency table of the scores, with groups 20–23, 24–27, 28–31, 32–35, and 36–39, find the group with the lowest frequency.

28 30 39 37 36 28 28 35 33 25
39 39 27 20 39 31 36 28 20 35
32 37 38 30 31 25 29 28 39 36
  • A32–35
  • B20–23
  • C24–27
  • D28–31
  • E36–39

Q25:

The table shows the marks of 100 students in a recent mathematics exam. What percentage of students received 30 marks or more?

Marks 0–9 10–19 20–29 30–39 40–49 50–59 Total
Frequency 8 22 15 22 16 17 100

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